A Course in Mathematical Statistics

A Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference.* Contains 25% new material* Includes the most complete coverage of sufficiency * Transformation of Random Vectors* Sufficiency / Completeness / Exponential Families* Order Statistics* Elements of Nonparametric Density Estimation* Analysis of Variance (ANOVA)* Regression Analysis* Linear Models

George G. Roussas earned a B.S. in Mathematics with honors from the University of Athens, Greece, and a Ph.D. in Statistics from the University of California, Berkeley. As of July 2014, he is a Distinguished Professor Emeritus of Statistics at the University of California, Davis. Roussas is the author of five books, the author or co-author of five special volumes, and the author or co-author of dozens of research articles published in leading journals and special volumes. He is a Fellow of the following professional societies: The American Statistical Association (ASA), the Institute of Mathematical Statistics (IMS), The Royal Statistical Society (RSS), the American Association for the Advancement of Science (AAAS), and an Elected Member of the International Statistical Institute (ISI); also, he is a Corresponding Member of the Academy of Athens. Roussas was an associate editor of four journals since their inception, and is now a member of the Editorial Board of the journal Statistical Inference for Stochastic Processes. Throughout his career, Roussas served as Dean, Vice President for Academic Affairs, and Chancellor at two universities; also, he served as an Associate Dean at UC-Davis, helping to transform that institution's statistical unit into one of national and international renown. Roussas has been honored with a Festschrift, and he has given featured interviews for the Statistical Science and the Statistical Periscope. He has contributed an obituary to the IMS Bulletin for Professor-Academician David Blackwell of UC-Berkeley, and has been the coordinating editor of an extensive article of contributions for Professor Blackwell, which was published in the Notices of the American Mathematical Society and the Celebratio Mathematica.

Concepts of Set TheorySome Probabilistic Concepts and ResultsOn Random variables and Their DistributionsDistribution Functions, Probability Densities, and their RelationshipsMoments of Random Variables-Some Moment and Probability InequalitiesCharacteristic Functions, Moment GeneratingFunctions, and Related TheoremsStochastic Independence with Some ApplicationsBasic Limit TheoremsTransformations of Random Variables and RandomVectorsOrder Statistics and Related TheoremsSufficiency and Related TheoremsPoint EstimationTesting HypothesesSequential ProceduresConfidence Regions-Tolerance IntervalsThe General Linear HypothesisAnalysis of VarianceThe Multivariate Normal DistributionQuadratic FormsNonparametric InferenceAppendicesTable of Selected Discrete and ContinuousDistributions and Some of their CharacteristicsSome Notation and Abbreviations